Notes on Sewall Wright: the Measurement of Kinship

David Burbridge continues his awesome series of posts on the history of evolutionary genetic thought with Notes on Sewall Wright: the Measurement of Kinship. Here's a taste:

In Malecot's system two genes at the same locus, in the same or different individuals, are defined as Identical by Descent (IBD) if they are both descended from the very same individual ancestral gene, without either of them undergoing mutation in the interim. The relatedness between two individuals can be measured, roughly speaking, by calculating the probability that two genes at the same locus in the two individuals are IBD. To do this it is necessary first to identify all the distinct paths of descent connecting the two individuals through a common ancestor, and then to calculate the probability that the same gene will have descended to both individuals from that ancestor along any given path. Since all such paths of descent are mutually exclusive (though portions of them may overlap), the resulting probabilities can be added together to give the total probability that a given gene in the two individuals is IBD. To take a simple case, consider two individuals (full siblings) who have both parents in common. I assume that the parents are not related to each other or inbred. If we select a (diploid autosomal) gene at random from one sibling, there is a probability of one-half that it comes from the mother, and, if it does, a probability of one-half that the same gene has descended from the mother to the other sibling. This gives a compound probability of one-quarter that the second sibling has received a gene from the mother that is IBD to the selected gene in the first sibling. There is likewise a probability of one-quarter that the second sibling has received an IBD copy from the father. The total probability is therefore one-half, which is often called the Coefficient of Relationship or Relatedness between full siblings. If the parents are themselves related or inbred (i.e. descended from one of their own ancestors by more than one possible path), additional paths of descent need to be taken into account. Since there are two genes at the relevant locus in the second sibling, there is a probability of one-quarter (one-half times one-half) that a particular one of these genes, chosen at random, is IBD to the selected gene in the first sibling. This is usually known as their Coefficient of Kinship. If a male and female with a non-zero Coefficient of Kinship mate together, there is a non-zero probability that any offspring will inherit two genes that are IBD to each other. This is usually known as the offspring's Coefficient of Inbreeding, and a little consideration shows that it is equal to the Coefficient of Kinship of the parents.